Strengthened SDP relaxation for an extended trust region subproblem with an application to optimal power flow

Anders Eltved; Samuel Burer

doi:10.1007/s10107-021-01737-9

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Strengthened SDP relaxation for an extended trust region subproblem with an application to optimal power flow

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Strengthened SDP relaxation for an extended trust region subproblem with an application to optimal power flow

Anders Eltved and Samuel Burer

Mathematical programming, Vol.197(1), pp.281-306

01/01/2023

DOI: 10.1007/s10107-021-01737-9

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Abstract

We study an extended trust region subproblem minimizing a nonconvex function over the hollow ball r≤ ‖ x‖ ≤ R intersected with a full-dimensional second order cone (SOC) constraint of the form ‖ x- c‖ ≤ bTx- a. In particular, we present a class of valid cuts that improve existing semidefinite programming (SDP) relaxations and are separable in polynomial time. We connect our cuts to the literature on the optimal power flow (OPF) problem by demonstrating that previously derived cuts capturing a convex hull important for OPF are actually just special cases of our cuts. In addition, we apply our methodology to derive a new class of closed-form, locally valid, SOC cuts for nonconvex quadratic programs over the mixed polyhedral-conic set { x≥ 0 : ‖ x‖ ≤ 1 }. Finally, we show computationally on randomly generated instances that our cuts are effective in further closing the gap of the strongest SDP relaxations in the literature, especially in low dimensions.

Combinatorics

Mathematics

Numerical Analysis

Calculus of Variations and Optimal Control; Optimization

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Mathematical and Computational Physics

Mathematical Methods in Physics

Mathematics and Statistics

Mathematics of Computing

Theoretical

Details

Title: Subtitle: Strengthened SDP relaxation for an extended trust region subproblem with an application to optimal power flow
Creators: Anders Eltved - Technical University of Denmark
Samuel Burer - University of Iowa
Resource Type: Journal article
Publication Details: Mathematical programming, Vol.197(1), pp.281-306
DOI: 10.1007/s10107-021-01737-9
ISSN: 0025-5610
eISSN: 1436-4646
Publisher: Springer Berlin Heidelberg
Language: English
Date published: 01/01/2023
Academic Unit: Business Analytics
Record Identifier: 9984380552302771

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